On the chromatic number of an infinitesimal plane layer

A. Ya Kanel-Belov, V. A. Voronov, D. D. Cherkashin

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This paper is devoted to a natural generalization of the problem on the chromatic number of the plane. The chromatic number of the spaces ℝn × [0, ε]k is considered. It is proved that 5 ≤ χ(ℝ2 × [0, ε]) ≤ 7 and 6 ≤ χ(ℝ2 × [0, ε]2) ≤ 7 for ε > 0 sufficiently small. Also, some natural questions arising from these considerations are posed.

Original languageEnglish
Pages (from-to)761-775
Number of pages15
JournalSt. Petersburg Mathematical Journal
Issue number5
StatePublished - 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.


  • Chromatic number of Euclidean spaces
  • Chromatic number of the plane


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